During a recent appearance on BBC's Question Time, Michael Gove, the secretary of state for education, extolled the importance of encouraging creativity in schools. He's right. Creativity is essential to the success and fulfilment of young people, to the vitality of our communities and to the long-term health of the economy. The trouble is that his current plans for the national curriculum seem likely to stifle the creativity of students and teachers alike. Consequently, anyone with a serious interest in student achievement, cultural vitality and economic sustainability should be deeply concerned.

We shouldn't be surprised when a politician says one thing and does another. The important issue here is that when he talks about creativity, Gove seems to mean what he says but to misunderstand what he's talking about. His views also suggest some serious misconceptions about teaching and learning in general. So what is creativity, and how does it work?

I define creativity as the process of having original ideas that have value. Creative work in any field often passes through typical phases. Sometimes what you end up with is not what you had in mind when you started. It's a dynamic process that often involves making new connections, crossing disciplines and using metaphors and analogies.

Creativity is about fresh thinking. It doesn't have to be new to the whole of humanity – though that's always a bonus – but certainly to the person whose work it is. Creativity also involves making critical judgments about whether what you're working on is any good, whether it's a theorem, a design or a poem.

There are various myths about creativity. One is that only special people are creative; another is that creativity is just about the arts; a third is that it's all to do with uninhibited "self-expression". None of these is true. On the contrary, everyone has creative capacities; creativity is possible in whatever you do, and it can require great discipline and many different skills.

I imagine Gove would agree with all of this. But his conclusions about how to promote creativity are very wide of the mark. On Question Time he had a lot to say about what's involved in being creative. He insists, for instance, that children have to learn the necessary skills before they can start to be creative. In English, he says, "creativity depends on mastering certain skills and acquiring a body of knowledge before being able to give expression to what's in you … You cannot be creative unless you understand how sentences are constructed, what words mean and how to use grammar."

In mathematics, "unless children are introduced to that stock of knowledge, unless they know how to use numbers with confidence, unless multiplication, long division, become automatic processes, they won't be able to use mathematics creatively … to make the discoveries which are going to make our lives better in the future".

Even if you're musically gifted, he says, "you need first of all to learn your scales. You need to secure a foundation on which your creativity can flourish." This all sounds like common sense. But like a lot of common sense it's wrong or, at best, a half-truth.

Over the past four years, I've spoken with many people about their particular talents and passions and how they discovered them. In my new book, Finding Your Element, I draw together some of the lessons they can teach us.Hans Zimmer is an Oscar-winning composer, who has created the scores for some of Hollywood's most successful films. As a child he loved to play the piano but had no patience for scales and rote learning. Whenever he tried to play or compose, his teacher would stop him and say: "Go and practise your scales!" He admits to being disruptive at school and was actually thrown out of eight of them. Finally, he arrived at number nine.

The headmaster took him to one side on the first day and said: "Look, I've read all these reports. How are we going to avoid this sort of trouble here? What is it you really want to do?" Hans said that all he really wanted to do was play music. With the head's support, he spent most of the time doing exactly that. Slowly he became engaged in other work too. He remembers a particularly brilliant teacher who took the class for German studies.

"He'd be sitting on his piano stool and he'd be talking about something and then he'd whip around and play the music of its period. Suddenly all this stuff started to come alive. Learning wasn't about learning things by heart and then regurgitating them like a bad cheese sandwich. He was fantastic."

It was the flexibility of that school and the inspiration of a few teachers that helped set Hans on the way to his extraordinary career. You might object that Hans is an exceptional case, but in several ways he is not.

First, creativity, like learning in general, is a highly personal process. We all have different talents and aptitudes and different ways of getting to understand things. Raising achievement in schools means leaving room for these differences and not prescribing a standard steeplechase for everyone to complete at the same time and in the same way.

Second, creativity is not a linear process, in which you have to learn all the necessary skills before you get started. It is true that creative work in any field involves a growing mastery of skills and concepts. It is not true that they have to be mastered before the creative work can begin. Focusing on skills in isolation can kill interest in any discipline. Many people have been put off mathematics for life by endless rote tasks that did nothing to inspire them with the beauty of numbers. Many have spent years grudgingly practicing scales for music examinations only to abandon the instrument altogether once they've made the grade.

The real driver of creativity is an appetite for discovery and a passion for the work itself. When students are motivated to learn, they naturally acquire the skills they need to get the work done. Their mastery of them grows as their creative ambitions expand. You'll find evidence of this process in great teaching in every discipline from football to chemistry.

Third, facilitating this process takes connoisseurship, judgment – and, yes, creativity, on the part of teachers. One concern about the revised national curriculum is that it will be too linear and prescriptive. For creativity to flourish, schools have to feel free to innovate without the constant fear of being penalised for not keeping with the programme. Too much prescription is a dead hand on the creative pulse of teachers and students alike.

Oddly, Gove seems to think he can improve schools by demeaning teachers. He can't. The evidence of high-performing systems around the world is that genuine school improvement depends on positive engagement with the profession. There's no other way. Unless he's prepared to teach everyone himself, he cannot improve education by vilifying educators.

When for the first time in their history two major teaching unions pass votes of no confidence in the secretary of state, he might pause a moment. A good general, it's said, doesn't fire on his own troops. Yet, to judge by his recent rant in the Daily Mail against "Marxist" professors, his head-butting with the unions and his condescension on Question Time to the shadow attorney general, he clearly revels in letting off fusillades against anyone who disagrees with him on education. An essential first step in being creative yourself is to question your own way of looking at things. If he's serious about promoting creativity in others, perhaps Gove could start there.